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The incident angles of the optical systems with high numerical apertures, such as lithography or microscope, are larger than those of normal ones. For these systems, polarized illumination is widely adopted. The coatings on their surfaces will make s and p polarization components of oblique incident light experience diverse amplitudes and phase modulations, and induce extra polarization aberrations. We apply the vectorial diffraction theory to assess the effects of coating-induced polarization aberrations on the focusing properties of these systems. By applying the generalized Debye integral, the relationship between the parameters of coating and electric field vector near the focal spot is established. Considering x linearly polarized light as the incident light field, we evaluate the potential influence of the coatings on the intensity and the full width at half maxium of focal spots. In the further discussion, we compare the results of different coatings when the various optimization goals are set, and certify that the phase difference caused by coating has more effect on focusing property. Based on this, the additional constraint conditions of coating design are proposed to suppress such disturbance, i.e. to properly increase relative weight of phase constraint conditions. With this proposed constraint conditions, we design and optimize an anti-reflection coating with low polarization aberrations. By applying this designing, the central intensity of focal spot can be enhanced by 12.5%, and the light energy utilization will be improved effectively.
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Keywords:
- optical coating /
- polarization aberrations /
- high numerical aperture
[1] Jasper H, Modderman T, Kerkhof M, C Wagner, Mulkens J, Boeij W de, Setten E van, Kneer B 2006 Opt. Microlith. XIX 6154 61541W-1
[2] Yu J J, Zhou C H, Jia W, Wu J, Lu Y C 2014 J. Opt. Soc. Am. A 31 1059
[3] Zhou G Q 2011 Chinese Phys. B 20 074203
[4] Lai K F, Rosenbluth A E, Han G, Tirapu-Azpiroz J, Meiring J, Goehnermeier A, Kneer B, Totzeck M, Zeiss C, Winter L de, Boeij W de, Kerkhof M Vde 2007 Opt. Microlith. XX 6520 D5200
[5] Flagello D G 2005 Adv. Microlith. Technol. 5645 44
[6] Wang Z L, Zhou M, Gao C Y, Zhang W 2012 Chinese Phys. B 21 064202
[7] Luo Z M, Chen S Z, Ling X H, Zhang J, Luo H L 2014 Acta. Phys. Sin. 63 13 (in Chinese) [罗朝明, 陈世祯, 凌晓辉, 张进, 罗海陆 2014 63 13]
[8] Hao X, Kuang C F, Wang T T, Liu X 2010 Opt. Lett. 35 3928
[9] Hao X, Kuang C F, Wang T T, Liu X 2010 J. Opt-Uk.,12
[10] Hao X, Kuang C F, Li Y H, Liu X 2012 Opt. Express 20 12692
[11] Deng S H, Liu L, Cheng Y, Li R X, Xu Z Z 2010 Opt. Express 18 1657
[12] Boruah B R, Neil M A A 2009 Opt. Commun. 282 4660
[13] Boruah B R, Neil M A A 2006 Opt. Express 14 10377
[14] Roichman Y, Waldron A, Gardel E, Grier D G 2006 Appl. Opt. 45 3425
[15] Richards B, Wolf E 1959 Proc R. Soc. Lon. Ser-A 253 358
[16] Quabis S, Dorn R, Eberler M, Glockl O, Leuchs G 2000 Opt. Commun. 179 1
[17] Davidson N, Bokor N 2004 Opt. Lett. 29 1318
[18] Li Y H, Shen W D, Zheng Z R, Zhang Y G, Liu X, Hao X 2011 J. Opt-Uk. 13 5
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[1] Jasper H, Modderman T, Kerkhof M, C Wagner, Mulkens J, Boeij W de, Setten E van, Kneer B 2006 Opt. Microlith. XIX 6154 61541W-1
[2] Yu J J, Zhou C H, Jia W, Wu J, Lu Y C 2014 J. Opt. Soc. Am. A 31 1059
[3] Zhou G Q 2011 Chinese Phys. B 20 074203
[4] Lai K F, Rosenbluth A E, Han G, Tirapu-Azpiroz J, Meiring J, Goehnermeier A, Kneer B, Totzeck M, Zeiss C, Winter L de, Boeij W de, Kerkhof M Vde 2007 Opt. Microlith. XX 6520 D5200
[5] Flagello D G 2005 Adv. Microlith. Technol. 5645 44
[6] Wang Z L, Zhou M, Gao C Y, Zhang W 2012 Chinese Phys. B 21 064202
[7] Luo Z M, Chen S Z, Ling X H, Zhang J, Luo H L 2014 Acta. Phys. Sin. 63 13 (in Chinese) [罗朝明, 陈世祯, 凌晓辉, 张进, 罗海陆 2014 63 13]
[8] Hao X, Kuang C F, Wang T T, Liu X 2010 Opt. Lett. 35 3928
[9] Hao X, Kuang C F, Wang T T, Liu X 2010 J. Opt-Uk.,12
[10] Hao X, Kuang C F, Li Y H, Liu X 2012 Opt. Express 20 12692
[11] Deng S H, Liu L, Cheng Y, Li R X, Xu Z Z 2010 Opt. Express 18 1657
[12] Boruah B R, Neil M A A 2009 Opt. Commun. 282 4660
[13] Boruah B R, Neil M A A 2006 Opt. Express 14 10377
[14] Roichman Y, Waldron A, Gardel E, Grier D G 2006 Appl. Opt. 45 3425
[15] Richards B, Wolf E 1959 Proc R. Soc. Lon. Ser-A 253 358
[16] Quabis S, Dorn R, Eberler M, Glockl O, Leuchs G 2000 Opt. Commun. 179 1
[17] Davidson N, Bokor N 2004 Opt. Lett. 29 1318
[18] Li Y H, Shen W D, Zheng Z R, Zhang Y G, Liu X, Hao X 2011 J. Opt-Uk. 13 5
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